Hotmail has a dreadful reputation. At the very least, I'd stay clear of it. Using it would make you look unprofessional.
One thing to watch out for is that if you're trying to send a large number of emails, many ISPs will assume you're a spammer. It sounds silly, but I've read plenty of horror stories about this.
One very important thing to consider with email newsletters is their deliverability - what percentage of them will actually REACH your subscribers. You want to make sure your newsletter will pass through the filters of ISPs and email outfits around the world. That's a very good reason for using a specialist service such as Aweber or GetResponse.
A good newsletter distribution company like Aweber will charge a modest fee and make things simple for you, even giving you the code to paste into your web page, so you don't even have to create a newsletter sign-up form. You'll save heaps of time, which you can then spend on marketing your newsletter, instead of wasting time researching how to set it up.
If you do manage to fiddle about doing things the hard, free way you suggested, you'll have problems when you grow. Imagine having a list of 5,000, 10,000 or so people. How will you handle that?
If you start in an amateurish way, later on when you grow, any respectable newsletter distribution service is unlikely to want you as a customer. You probably won't be able to transfer those email addresses to Aweber, for example, because it has very strict rules to protect its reputation as a non-spammer.
I strongly recommend that you start with a good, reliable system. I may be wrong, but I doubt very much if you can do that free.